1. Microeconomics Course E John Hey

2. Examinations Go to http://www.luiss.it/hey/microeconomia/esami.htmhttp://www.luiss.it/hey/microeconomia/esami.htm Read http://www.luiss.it/hey/microeconomia/detesen.htm Check on Answer Sheet Check on Aide/Memoire Check on grids

3. Aide-Memoire

4. Grids 1

5. Grids 2

6. Answer Sheet Answer sheet

7. Example 1 of Exams Appello1 Traccia 1 1-4: demand and supply 5-7: Edgeworth Box 8,9: finding consumer demands 10,11: finding firm demands 12,13: competitive firm 14,15: monopoly 16,17: game theory

8. 1-4: demand and supply Consider a market for a hypothetical good in which there are a number of buyers and sellers, each of which wants to buy or sell one unit of the good. Assume that a buyer who is indifferent about buying always buys and a seller who is indifferent about selling always sells. The reservation prices are given below, first for the buyers and then for the sellers. Buyers: 7, 6, 8, 5, 7. Sellers: 2, 6, 3, 3, 7, 7, 4.

9. Question 1: What is the maximum quantity demanded? (a) 5 (b) 12 (c) 6 (d) 7 Question 2: What is the maximum quantity supplied? (a) 7 (b) 4 (c) 5 (d) 12 Question 3: What is the competitive equilibrium price (specify a range if more than one equilibrium price)? (a) 4 (b) 7 (c) 6 (d) Any price between 5 and 6 Question 4: What is the quantity exchanged in the competitive equilibrium? (a) 5 (b) 2 (c) 4 (d) 3

12. Questions 5-7 Consider, in an Edgeworth Box, exchange between two individuals, Individual A and Individual B, with preferences as specified below, endowed with two goods, Good 1 and Good 2. (Consider only competitive equilibrium in which at least one individual is better off compared to the initial position.) Individual A has Perfect Complement preferences with parameter a = 1. Individual B has Perfect Complement preferences with parameter a = 2. Total endowment of good 1 is 6 and that of good 2 is 8. Individual A's endowment of good 1 is 2 and that of good 2 is 7.

13. Question 5: What is the competitive equilibrium price ratio? (a) 1.00 (b) 1.50 (c) 1.33 (d) 3.50 Question 6: What is the quantity exchanged of good 1 to reach the competitive equilibrium? (a) 4.00 (b) 2.00 (c) 3.00 (d) 1.00 Question 7: What is the quantity exchanged of good 2 to reach the competitive equilibrium? (a) 1.00 (b) 1.50 (c) 2.00 (d) 3.00

21. Questions 8 and 9 In the next two questions you will be asked questions about the demands of an individual with the following preferences at the following incomes and prices. The individual has Perfect Complement preferences with parameter a = 1.00. The individual has income 10 and faces prices 1.00 and 1.00 for goods 1 and 2. Question 8: What is the individual's demand for Good 1? 5.20 5.00 10.00 0.00 Question 9: What is the individual's demand for Good 2? 5.00 10.00 5.20 0.00

22. Questions 10 and 11 In the next two questions you will be asked to consider a firm with constant returns to scale technology. You will be told the technology, the desired output and the factor prices that the firm faces. You will be asked to work out the firms' demand for the two factors. The technology is Perfect Substitutes with parameter a = 1.00. The firm produces output 30 and faces factor prices 2.00 and 2.00 for factors 1 and 2. Question 10: What is the firm's demand for factor 1? 0.00 Any point on the isoquant for the level of output required 30.00 15.00 Question 11: What is the firm's demand for factor 2? Any point on the isoquant for the level of output required 30.10 60.00 30.00

23. Questions 12 and 13 In the next two questions you will be asked to consider a competive firm which has a cost function C(y) = a + b*y + c*y^2 where a, b and c are given below. a = 10.0, b = 0.0, c = 2.0. Suppose that the price of the firm's output is 40. Question 12: Determine the optimal output of the firm. 40.00 0.00 10.00 20.25 Question 13: What is the firm's profit? 0.00 190.00 809.88 400.00

24. Questions 14 and 15 In the next two questions you will be asked to consider a monopoly with a demand curve for its output given by p = a - b*y where p and y denote the price and quantity of its output and where a and b are given below. Suppose that the cost function of the firm is given by C(y) = c + d*y where c and d are given below. Assume that the monopolist always has to pay its fixed costs. a = 20, b = 1. c = 20, d = 10 Question 14: What price does the monopoly set if it wants to maximise its profits? 15.00 20.00 0.00 10.00 Question 15: What output does the monopoly optimally produce? 0.00 10.00 11.00 5.00

25. Questions 16 and 17 In the next two questions you will be asked to consider a game played simultaneously, and without communication between two players, 1 and 2, each of whom can choose one of two options A and B. The payoffs to the two players are given below, the first for Player 1 and then for Player 2. The order of the payoffs is AA, AB, BA, BB where XY indicates the outcome when Player 1 plays X and Player 2 plays Y. Player 1: 1, 7, 3, 10. Player 2: 4, 9, 6, 10. Question 16: Specify ALL the Nash Equilibria in pure strategies. BA AA There are none BB Question 17: Specify ALL other outcomes (not a Nash Equilibrium) that Pareto dominate any of these. AA dominates BA BA dominates AA There are none BA e AA dominates AB

26. Tips! Remember that you get 2 marks for a correct answer and lose 1 mark for an incorrect. DO NOT GUESS! Take coloured pencils and pens. Take a rubber. Do NOT apply MAGIC formulae. Good Luck!!